Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach

• URL: http://arxiv.org/abs/2403.18617v1
• Date: Wed, 27 Mar 2024 14:32:03 GMT
• Title: Quantum concentration inequalities and equivalence of the thermodynamical ensembles: an optimal mass transport approach
• Authors: Giacomo De Palma, Davide Pastorello,
• Abstract summary: We prove new concentration inequalities for quantum spin systems. Our results do not require the spins to be arranged in a regular lattice. We introduce a local W1 distance, which quantifies the distinguishability of two states with respect to local observables.
• Score: 4.604003661048267
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We prove new concentration inequalities for quantum spin systems which apply to any local observable measured on any product state or on any state with exponentially decaying correlations. Our results do not require the spins to be arranged in a regular lattice, and cover the case of observables that contain terms acting on spins at arbitrary distance. Moreover, we introduce a local W1 distance, which quantifies the distinguishability of two states with respect to local observables. We prove a transportation-cost inequality stating that the local W1 distance between a generic state and a state with exponentially decaying correlations is upper bounded by a function of their relative entropy. Finally, we apply such inequality to prove the equivalence between the canonical and microcanonical ensembles of quantum statistical mechanics and the weak eigenstate thermalization hypothesis for the Hamiltonians whose Gibbs states have exponentially decaying correlations.

Related papers

• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning [0.23301643766310368]
  We show that spin chains in thermal equilibrium have a correlation structure in which individual regions are strongly correlated at most with their near vicinity. We prove that these measures decay superexponentially at every positive temperature.
  arXiv  Detail & Related papers  (2024-02-28T17:28:01Z)
• From decay of correlations to locality and stability of the Gibbs state [0.27309692684728604]
  We show that whenever a Gibbs state satisfies decay of correlations, then it is stable, in the sense that local perturbations influence the Gibbs state only locally. These implications hold true in any dimension, only require locality of the Hamiltonian and rely on Lieb-Robinson bounds.
  arXiv  Detail & Related papers  (2023-10-13T15:20:58Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• Quantum concentration inequalities [12.56413718364189]
  We establish transportation cost inequalities (TCI) with respect to the quantum Wasserstein distance. We prove Gibbs states of commuting Hamiltonians on arbitrary hypergraphs $H=(V,E)$ satisfy a TCI with constant scaling as $O(|V|)$. We argue that the temperature range for which the TCI holds can be enlarged by relating it to recently established modified logarithmic Sobolev inequalities.
  arXiv  Detail & Related papers  (2021-06-30T05:44:12Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• Long-distance entanglement of purification and reflected entropy in conformal field theory [58.84597116744021]
  We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy. We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
  arXiv  Detail & Related papers  (2021-01-29T19:00:03Z)
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions [2.148535041822524]
  We prove a strong exponential convergence in relative entropy of the system to equilibrium under a condition of spatial mixing. We show that our notion of spatial mixing is a consequence of the recent quantum generalization of Dobrushin and Shlosman's complete analyticity of the free-energy at equilibrium. Our results have wide-ranging applications in quantum information.
  arXiv  Detail & Related papers  (2020-09-24T16:54:06Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Intrinsic decoherence effects on measurement-induced nonlocality [1.5630592429258865]
  We study the dynamics of entanglement quantified by the concurrence and measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm. We show that the existence of quantum correlation captured by MIN in the unentangled state.
  arXiv  Detail & Related papers  (2020-05-13T16:18:25Z)
• Entanglement as upper bounded for the nonlocality of a general two-qubit system [16.676050048472963]
  We systematically investigate the relationship between entanglement and nonlocality of a general two-qubit system. We find that the nonlocality of two different two-qubit states can be optimally stimulated by the same nonlocality test setting.
  arXiv  Detail & Related papers  (2020-04-17T16:42:27Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.